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Mixed Problem for Even-Order Differential Equations with an Involution

Владикавказский математический журнал
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Oscillation Criteria for Even-Order Neutral Differential Equations

Applied Mathematics Letters, 2016
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Tongxing Li, Yuriy V Rogovchenko
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OSCILLATION OF EVEN-ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH AN ADVANCED ARGUMENT

Functional Differential Equations, 2023
Thispaperdealswiththeoscillatory eha io ro sol tio stoaclasso e e order o li eardiffere tial e atio swithada cedar e ts. efi dasi le co ditio thate s restheoscillatio o thest diede atio . Ea plesarepro idedto de o stratethe ai fi di s. Keywords: da ceddiffere tiale atio ,Oscillatio ,No li ear,Ee order. MSC(2020)34 11,34 10.
Grace, S., Chhatria
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Lyapunov-Type Inequality for a Class of Even-Order Differential Equations

Applied Mathematics and Computation, 2010
The paper concerns necessary conditions for the existence of nonzero solutions of the \(2n\)-order linear differential equation \[ \left(r_{2n-1}\left(t\right)\left(r_{2n-2}\left(t\right)\left(\cdots\left(r_2\left(t\right)\left(r_1\left(t\right) x^\prime\right)^\prime\right)^\prime\cdots\right)^\prime\right)^\prime\right)^\prime+q\left(t\right)x=0 ...
Kueiming Lo
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On periodic solutions for even order differential equations

Nonlinear Analysis: Theory, Methods & Applications, 2008
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Chen, Jinhai, O'Regan, Donal
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Disconjugacy Criteria for Nonselfadjoint Differential Equations of Even Order

Canadian Journal of Mathematics, 1971
Disconjugacy criteria have been established for linear selfadjoint differential equations of order 2n by Sternberg [4] and Ahlbrandt [1]. Such differential equations can be written in the form1.1where it is assumed that the coefficients are real and that Pn(x) ≠ 0.
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Oscillation Theorems for Nonlinear Ordinary Differential Equations of Even Order

Canadian Mathematical Bulletin, 1981
Consider the differential equation1wherenis even andf(t, y)is subject to the following conditions:(a)f(t, y)is continuous on [0, ∞)×R;(2) (b)f(t, y)is nondecreasing inyfor each fixedt∈[0,∞);(c)yf(t, y )> 0 fory≠ 0 andt∈[0,∞).
Kreith, Kurt, Kusano, Takasi
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Ordinary Differential Equations of Even Order with Integral Conditions

Doklady Mathematics
We consider an even-order ordinary differential operator with a spectral parameter and integral conditions. An a priori estimate of the solutions to the problem is obtained for sufficiently large values of the spectral parameter. The discreteness and the sectoral structure of the spectrum of the corresponding operators are proved.
R. A. Bayrash, A. L. Skubachevskii
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Oscillation criteria for even order differential equations

Annali di Matematica Pura ed Applicata, 1964
Three theorems concerning oscillatory properties of solutions of even order ordinary differential equations are given. One theorem gives sufficient conditions for all solutions of (*) y(2n)(x) + f(y(x))p(x) = 0 to possess an infinite number of zeroes on the positive x axis.
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Periodic solutions of a class of even order differential equations

1996
Summary: We investigate sufficient conditions for the non-existence of periodic solutions of equation (1) with \(p\equiv 0\), \(f_{2r} (0)=0\) and sufficient conditions for existence of periodic solutions of equation (1) \[ \begin{multlined} x^{(2r)} +a_1x^{(2r-1)} +a_2 x^{(2r-2)} +\cdots +a_{2r-3} \ddot x+f_{2r-2} (\dot x) \dddot x+f_{2r-1} (x)\dot x ...
Tejumola, H.O., Iyase, S.A .
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